IDKMesh

Reproducing E017: when 25 verifiers behaved like one

E017 is IDKMesh’s retained experiment on measured verifier dependence. It does not use synthetic reviewer votes for its headline result: 25 deterministic partial test oracles vote on a 72-candidate corpus whose correctness is decided by executable hidden tests.

The main result is deliberately narrow:

On this programmatic verifier panel, majority voting over 25 reviewers produced an error rate of 0.2083, compared with 0.2044 for a single average verifier. The measured effective panel size was therefore 1.00 of 25.

The experiment also found that changing the aggregation rule mattered much more than adding reviewers: requiring at least 24 of 25 acceptance votes reduced the observed error to 0.0556, about 3.7x below majority vote.

This page gives the shortest reproducible path to those numbers, the retained artifact identity, and the conditions under which the interpretation should be revised.

Retained experiment

Canonical record:

Retained vote artifact:

Reproduction code:

The experiment and analyzer use the Python standard library. The analysis does not need a network connection or an external model API.

1. Verify that you have the retained artifact

From a clean repository checkout:

git hash-object experiments/results/E017-partial-oracle-votes.jsonl.gz

Expected Git blob SHA:

0b710ba6d376da6a688edcc0cab9bf6fb98e322a

A different hash means you are not analyzing the retained E017 vote artifact described on this page. That does not make the new artifact invalid, but it is a different reproduction input and should be reported as such.

2. Run the pinned mechanism tests

python -m pytest -q \
  tests/test_e017_item_difficulty.py \
  tests/test_e017_oracles.py

These tests check properties such as deterministic seeded draws, distinct input regions, the panel-model probability distributions, and the item-difficulty fit machinery. Passing them verifies the analysis mechanism; it does not by itself reproduce the observed panel result.

3. Analyze the retained votes

python sim/e017_analyze.py \
  experiments/results/E017-partial-oracle-votes.jsonl.gz \
  --trials 200000

The high-value acceptance checks are:

Quantity Retained E017 value
Verifiers 25
Verifiers discriminating above chance 25 / 25
Mean verifier accuracy 0.7956
Mean within-region error correlation 0.8924
Mean cross-region error correlation 0.5263
Mean all-pairs error correlation 0.5873
Majority-vote panel error 0.2083
Single-average-verifier error 0.2044
Measured effective panel size 1.00 of 25
N/(1+(N-1)rho) heuristic 1.66
24-of-25 acceptance error 0.0556

The stochastic model checks inside the analyzer use fixed seeds. Tiny platform-level floating-point differences are possible; the interpretation should not depend on the last decimal place.

4. Regenerate the vote panel

The retained artifact is enough to reproduce the published analysis. To rerun the verifier panel itself:

python sim/e017_verify.py \
  --seeds 5 \
  --draws 6 \
  --out /tmp/e017-votes.jsonl

Then analyze the regenerated file:

python sim/e017_analyze.py /tmp/e017-votes.jsonl --trials 200000

The panel is five input regions by five seeds: 25 verifiers. The corpus has 72 candidate solutions from 24 problems.

Do not compare the gzip byte hash of a newly compressed file to the retained artifact unless compression metadata is normalized. Compare the vote semantics and analysis outputs instead.

What was actually observed

Declared diversity did not imply independence

Verifiers in the same declared input region had mean error correlation 0.8924. Verifiers in different declared regions still had mean error correlation 0.5263. The region label was informative but did not create an independence boundary.

Majority vote added almost no protection

The 25-verifier majority-vote error was 0.2083. The mean single-verifier error was 0.2044. Mapping the observed panel error back to an idealized independent panel gave an effective size of 1.00, despite 25 nominal members.

The common approximation N_eff = N / (1 + (N - 1) rho) returned 1.66, still 1.66x above the measured effective size on this panel.

The shape of dependence mattered

A flat shared-shock model parameterized by the measured mean correlation predicted a majority error around 0.1216, about 1.7x below the observed 0.2083.

A beta-binomial item-difficulty model at the same parameter count reproduced the partial-failure shape much better and predicted a panel error of 0.1847. E020 later qualified that model too: it still under-predicts the observed unanimity floor.

The useful conclusion is not that the beta-binomial is universally correct. It is that one pairwise correlation coefficient is not sufficient to describe this panel’s error geometry.

Quorum choice mattered more than panel size

These partial test oracles had one-sided errors: a verifier could miss a defect, but the experiment observed zero false rejects of correct candidates.

Acceptance threshold Observed error
1 of 25 0.4167
13 of 25 — majority 0.2083
19 of 25 0.0972
24 of 25 0.0556
25 of 25 0.0556

Changing majority to a 24-of-25 requirement reduced error by about 3.7x. Four defective candidates remained invisible to every verifier, producing an irreducible floor that no quorum could remove.

What this result does not establish

E017 should not be cited as evidence that 25 LLM judges equal one judge.

The measured verifiers are programs, not people or LLMs. Their diversity structure is deliberately constructed from input regions and random seeds. Their errors are one-sided because they are partial test oracles. The corpus is 72 candidates from 24 independent problems, all at Python function level.

IDKMesh separately attempted an LLM-verifier correlation experiment in E016. That panel failed its competence screen, so its near-zero correlation could not be interpreted as independence.

The transferable E017 lesson is narrower:

Measure reviewer competence and shared error structure before converting reviewer count into an evidence claim.

What would revise the current interpretation

A useful reproduction should be allowed to disagree. The interpretation should be revised if, under a correctly matched implementation and corpus:

  1. the retained artifact no longer produces the stated headline metrics;
  2. independently implemented analysis finds a materially different panel error or correlation structure;
  3. a replicated verifier construction produces low cross-region dependence and a majority-vote gain consistent with genuinely independent reviewers;
  4. the apparent 3.7x quorum improvement disappears after correcting a bug, leakage, or hidden-test error;
  5. broader corpora show that the observed item-difficulty/floor behavior is specific to these 24 problems.

A disagreement should be published with the code, artifact identity, corpus, and exact aggregation rule. Failed reproduction is useful evidence.

How to cite or reuse the result

For a technical discussion, link to this reproduction note and the canonical E017 record. If using IDKMesh software or evidence contracts, the repository also provides CITATION.cff.

When reusing the headline number, preserve the scope:

In IDKMesh E017, 25 independently seeded programmatic partial test oracles had a measured effective panel size of 1.00 under majority vote on a 72-candidate / 24-problem corpus.

Do not shorten that to a universal statement about human or LLM review panels.

Last reviewed: 2026-09-24.